The AM frequencies of a radio dial range from 550 kHz, and the FM frequencies range of 88.0 MHz to MHz. all of these radio waves travel at a speed of 3.0x10^8 m/s, what are the wavelenght ranges of a.) the aM brand b.) FM brand
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To find the wavelength range for both the AM and FM frequencies, we can use the formula:
Wavelength (λ) = Speed of Light (c) / Frequency (f)
a) AM Brand:
The frequency range for AM frequencies is given as 550 kHz (kiloHertz), which can be converted to Hz by multiplying it by 10^3. Therefore, the range for AM frequencies is from 550 kHz to 1600 kHz (1.6 MHz).
Using the speed of light (c) = 3.0x10^8 m/s, we can calculate the wavelength range for AM frequencies as follows:
For 550 kHz:
λ = c / f = (3.0x10^8 m/s) / (550x10^3 Hz) = 545.45 meters
For 1600 kHz:
λ = c / f = (3.0x10^8 m/s) / (1600x10^3 Hz) = 187.5 meters
Therefore, the wavelength range for the AM brand is approximately 545.45 meters to 187.5 meters.
b) FM Brand:
The frequency range for FM frequencies is given as 88.0 MHz (megaHertz) to MHz. To represent the range, let's consider the upper limit of the frequency range as f2 (higher frequency) and the lower limit as f1 (lower frequency).
Using the speed of light (c) = 3.0x10^8 m/s, we can calculate the wavelength range for FM frequencies as follows:
For 88.0 MHz:
λ1 = c / f1 = (3.0x10^8 m/s) / (88.0x10^6 Hz) = 3.41 meters
For f2 MHz:
λ2 = c / f2 = (3.0x10^8 m/s) / (f2x10^6 Hz) - where you can substitute f2 with the desired value
Therefore, the wavelength range for the FM brand starts from approximately 3.41 meters and goes up to λ2 meters (which depends on the upper limit frequency provided in MHz).